Exponent Quiz - Level 1
(4x⁵)³
(4x⁵)³ = 4x⁵ * 4x⁵ * 4x⁵ = 64x¹⁵ Again, you can expand the problem in order to solve it (as above), or you could raise every term inside the parentheses to the 3rd power, so 4³ = 64 and (x⁵)³ = x¹⁵
(x⁵)⁶
(x⁵)⁶ = x⁵ * x⁵ * x⁵ * x⁵ * x⁵ * x⁵ = x³⁰ You can expand the problem in order to solve it (as above), or you could raise x⁵ to the 6th power by multiplying the exponents. 5*6 = 30, which becomes the new exponent.
Rewrite the problem below as 2 to the power of an exponent. 2 * 2 * 2 * 2 * 2 * 2 * 2
2 * 2 * 2 * 2 * 2 * 2 * 2 = 2⁷
(2x⁴)⁴
2x⁴ * 2x⁴ * 2x⁴ * 2x⁴ = 16x¹⁶
2x⁴ⁿ⁻² * 3x⁷ⁿ⁺⁹
2x⁴ⁿ⁻² * 3x⁷ⁿ⁺⁹ = 6x¹¹ⁿ⁺⁷
2x⁹ * 3x²
2x⁹ * 3x² = 6x¹¹
2⁴ * 2⁸
2¹²
2⁵ * 2³ * 2⁴
2⁵ * 2³ * 2⁴ = 2¹²
(3x²)³
3x² * 3x² * 3x² = 27x⁶ You can expand the problem in order to solve it (as above), or you could raise every term inside the parentheses to the 3rd power, so 3³ = 27 and (x²)³ = x⁶
4x⁶ * 6x⁸
4x⁶ * 6x⁸ = 24x¹⁴
7 * 7⁻² * 7
7⁰ = 1 Remember that if a term doesn't have an exponent, the implied exponent is 1. So 7 = 7¹
x * x * x
x³
x³ / x⁻²
x³⁻⁻² = x³⁺² = x⁵
(x⁴)¼
x¹ = x
x⁵ * x²
x⁷
x³ / x⁵
x⁻²
x⁴ / x¹⁰
x⁻⁶ = 1 / x⁶
x / x⁴
x / x⁴ = x¹ / x⁴ = x¹⁻⁴ = x⁻³ = 1/x³
x * x
x²
x⁵ / x³
x²